It is difficult to answer your question without better photos or an exam. You need to be able to see the proportion of your mouth and face with your eyes, and in profile and other views. In terms of the photo that you have posted, the mouth appears to be good width with relation to your nasal width. There is no good cosmetic treatment to "widen" your mouth. I would consider having an oral exam from a dentist, orthodontist, or plastic surgeon who understands how occlusion and dental relationships can help your mouth posture. They will also look at your facial symmetry and proportion overall. Dentofacial procedures that are excellent for facial symmetry and harmony are extremely effective and powerful.
Thank you for your question and photograph. I think that your lips are well proportioned to your face but a small amount of dermal filler placed into your lower lip may achieve an improved upper to lower lip volume balance, but this is strictly a person decision for you to make. One can not make the lips longer or wider through surgery but some camouflaging can be done with dermal fillers. Every person has some subtle asymmetry between the left and right sides of their face but speak to an ASPS board certified plastic surgeon to voice your concerns.